Maps and measurements of the J=1-0, J=2-1, J=3-2, J=4-3 12CO, the J=1-0, J=2-1 and J=3-2 13CO lines in the central arcminute squared of NGC 278, NGC 660, NGC 3628, NGC 4631, and NGC 4666, as well as 492 GHz [CI] maps in three of these are used to model the molecular gas. All five objects exhibit bright CO emission in the inner regions, with strong central concentrations in NGC 660, NGC 3628, and NGC 4666, but not in the weakest CO emitters NGC 278 and NGC 4631. In all cases, the observed lines

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... ould be modeled only with at least two distinct gas components. The physical condition of the molecular gas is found to differ from galaxy to galaxy. Relatively tenuous (density 100-1000 cm-3) and high kinetic temperature (100-150 K) gas occurs in all galaxies, except perhaps NGC 3628, and is mixed with cooler (10-30 K) and denser (3000-10000 cm-3) gas. In all galaxy centers, the CO-to-H2 conversion factor X is typically an order of magnitude smaller than the 'standard' value for the Solar Neighborhood. The molecular gas is constrained within radii between 0.6 and 1.5 kpc from the nuclei. Within these radii, H2 masses are typically 0.6-1.5 x 10**8 M(O), which corresponds to no more than a few per cent of the dynamical mass in the same region.